Question

given ( l parallel m parallel n ), find the value of ( x ).

Explanation:

Step1: Use the property of adjacent angles

Since \( l\parallel m\parallel n\), the angle of \(124^{\circ}\) and \((5x - 4)^{\circ}\) are adjacent angles on the same - side of the transversal. The sum of adjacent angles on the same - side of the transversal for parallel lines is \(180^{\circ}\). So, we have the equation \(124+(5x - 4)=180\).

Step2: Simplify the equation

Simplify the left - hand side of the equation: \(124+(5x - 4)=124 + 5x-4=5x + 120\). So the equation becomes \(5x+120 = 180\).

Step3: Solve for \(x\)

Subtract \(120\) from both sides of the equation: \(5x+120-120=180 - 120\), which gives \(5x=60\). Then divide both sides by \(5\): \(x=\frac{60}{5}=12\).

Answer:

\(12\)